What are the character sketches of Duke Senior and Duke Frederick in the play As You Like It by Shakespeare?

One of the simplest ways to analyze these two is to
compare and contrast them.  First, they are brothers and caught up in a bit of a
struggle for power.  Duke Frederick is the younger, but holds the power at the opening
of the play, having banished his elder brother Duke
Senior.

For similarities, both are fathers:  Duke Frederick
is the father of Celia and Duke Senior of Rosalind.  Both are also actually rulers of
their dominions:  Duke Frederick at court and Duke Senior in the Forest of
Arden.

But they are very different men.  Duke Senior is the
rightful Duke, but as he has been banished by his brother, he sets up a Utopian society
in the forest which he rules, sort of like Robin Hood (without the stealing).  He is
good and virtuous.

Duke Frederick is sneaky, full of
intrigues and a bit devoid of motivation for his actions.  He represents all the power
plays and back-stabbings of a political life.  We can recognize the potential for this
even in our politicians today when we observe that "power" can
corrupt.

This being a Comedy in which a world turned
topsy-turvey is made right at the end of the play, Duke Senior is restored to his
rightful place of power.  And Duke Frederick repents and relents, restoring balance and
harmony to the world of the play.